Computational Cost Reduction in Learned Transform Classifications

We present a theoretical analysis and empirical evaluations of a novel set of techniques for computational cost reduction of classifiers that are based on learned transform and soft-threshold. By modifying optimization procedures for dictionary and classifier training, as well as the resulting dictionary entries, our techniques allow to reduce the bit precision and to replace each floating-point multiplication by a single integer bit shift. We also show how the optimization algorithms in some dictionary training methods can be modified to penalize higher-energy dictionaries. We applied our techniques with the classifier Learning Algorithm for Soft-Thresholding, testing on the datasets used in its original paper. Our results indicate it is feasible to use solely sums and bit shifts of integers to classify at test time with a limited reduction of the classification accuracy. These low power operations are a valuable trade off in FPGA implementations as they increase the classification throughput while decrease both energy consumption and manufacturing cost.

[1]  Jean Ponce,et al.  Task-Driven Dictionary Learning , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[3]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[4]  Yoshua Bengio,et al.  Training deep neural networks with low precision multiplications , 2014 .

[5]  Pascal Vincent,et al.  Representation Learning: A Review and New Perspectives , 2012, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Francesco Piazza,et al.  Fast neural networks without multipliers , 1993, IEEE Trans. Neural Networks.

[7]  Alex Krizhevsky,et al.  Learning Multiple Layers of Features from Tiny Images , 2009 .

[8]  I. Johnstone,et al.  Ideal spatial adaptation by wavelet shrinkage , 1994 .

[9]  Rama Chellappa,et al.  Analysis sparse coding models for image-based classification , 2014, 2014 IEEE International Conference on Image Processing (ICIP).

[10]  Sachin S. Talathi,et al.  Fixed Point Quantization of Deep Convolutional Networks , 2015, ICML.

[11]  Emerson Lopes Machado,et al.  Redução de custo computacional em classificações baseadas em transformadas aprendidas , 2016 .

[12]  Erkki Oja,et al.  Reduced Multidimensional Co-Occurrence Histograms in Texture Classification , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Kevin K Dobbin,et al.  Optimally splitting cases for training and testing high dimensional classifiers , 2011, BMC Medical Genomics.

[14]  Jürgen Schmidhuber,et al.  Deep learning in neural networks: An overview , 2014, Neural Networks.

[15]  Yoshua Bengio,et al.  Neural Networks with Few Multiplications , 2015, ICLR.

[16]  Pritish Narayanan,et al.  Deep Learning with Limited Numerical Precision , 2015, ICML.

[17]  Bernhard Pfahringer,et al.  Compression-Based Discretization of Continuous Attributes , 1995, ICML.

[18]  Pascal Frossard,et al.  Dictionary Learning for Fast Classification Based on Soft-thresholding , 2014, International Journal of Computer Vision.

[19]  Xiaoming Huo,et al.  Uncertainty principles and ideal atomic decomposition , 2001, IEEE Trans. Inf. Theory.

[20]  Chee Kheong Siew,et al.  Extreme learning machine: Theory and applications , 2006, Neurocomputing.

[21]  R. Siezen,et al.  others , 1999, Microbial Biotechnology.

[22]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[23]  Yoshua Bengio,et al.  Deep Sparse Rectifier Neural Networks , 2011, AISTATS.

[24]  Yoshua Bengio,et al.  BinaryConnect: Training Deep Neural Networks with binary weights during propagations , 2015, NIPS.

[25]  Geoffrey E. Hinton,et al.  On rectified linear units for speech processing , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[26]  Yoram Bresler,et al.  Learning Sparsifying Transforms , 2013, IEEE Transactions on Signal Processing.

[27]  Ran El-Yaniv,et al.  Binarized Neural Networks , 2016, NIPS.

[28]  Andrew L. Maas Rectifier Nonlinearities Improve Neural Network Acoustic Models , 2013 .

[29]  Geoffrey E. Hinton,et al.  Rectified Linear Units Improve Restricted Boltzmann Machines , 2010, ICML.

[30]  Jack J. Dongarra,et al.  From CUDA to OpenCL: Towards a performance-portable solution for multi-platform GPU programming , 2012, Parallel Comput..